Top senators who have been quietly revising a controversial overhaul of criminal justice laws unveiled their reworked compromise on Thursday that they believe addresses conservative criticisms that could have derailed the bill in the Senate.

Influential Senate Democrats and Republicans held a news conference trumpeting the changes and to try and show a renewed sense of momentum behind the long-stalled legislation that tries to ease mandatory minimum sentences for nonviolent offenders.

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“Obviously, reaching a consensus hasn’t been easy,” Senate Judiciary Committee Chairman Chuck Grassley (R-Iowa) said. “But as you can see, we have a remarkable group of senators supporting the bill. We believe that it truly addresses in a bipartisan way the concerns that had been brought forward.”

Senate Minority Whip Dick Durbin of Illinois, the top Democratic co-sponsor of the bill, added: “This is the best chance in a generation to reform our criminal drug sentencing laws.”

Republican Sens. Dan Sullivan of Alaska and Steve Daines of Montana are among the new co-sponsors of the revised legislation. GOP Sens. Mark Kirk of Illinois and Thad Cochran of Mississippi also endorsed the bill after changes were made in recent weeks. New Democratic backers include Sens. Michael Bennet of Colorado, Joe Manchin of West Virginia and Bill Nelson of Florida.

The original version passed the Senate Judiciary Committee 15-5 in October, but tough-on-crime Senate conservatives — led by Sen. Tom Cotton of Arkansas — warned that it would inadvertently release felons with violent criminal records early from prison. Sen. Ted Cruz (R-Texas) was also a vocal critic of the bill — which the first endorser of his presidential campaign in the Senate, Mike Lee of Utah, helped draft — but has been quiet lately as he’s been campaigning.

The compromise won’t satisfy critics like Cotton, but nevertheless has been enough to sway a handful of other Republicans and to get influential organizations, such as the National District Attorneys Association, on board.

For instance, one section of the original legislation to reduce enhanced mandatory minimum sentences for people convicted under the Armed Career Criminals Act has been eliminated. The bill also now says that other reduced mandatory minimum sentences won’t apply retroactively for anyone who has been convicted of any serious violent felony. And it adds enhanced mandatory sentences for crimes involving Fentanyl, an opioid drug.

The influential district attorneys group wrote to Senate leaders earlier this week, saying the revised version “filters out the truly dangerous individuals” so they don't benefit from the reduced mandatory minimum sentences.

But the revisions weren’t enough to persuade some Republicans whom backers targeted. Sen. David Perdue of Georgia, seen by some proponents as a potential supporter, argued that the revisions would still allow serious drug traffickers to be released early from prison.

“Proponents of this criminal-leniency bill have waged a disinformation campaign because they simply want to reduce the number of people in federal prison,” Perdue said.

That prompted FreedomWorks, one of the major conservative outside groups backing the Senate measure, to fire back at Perdue, calling the Georgia senator’s comments on the legislation “misleading and hypocritical.”

“The changes unveiled Thursday are reasonable and will promote public safety, which is why conservatives like Sens. Mike Lee, Tim Scott and Rand Paul support this bill,” said Jason Pye, FreedomWorks’ communications director. “In fact, many of the sentencing reforms in this bill ... are similar to those found in the Smarter Sentencing Act, of which Perdue is a co-sponsor.”

FreedomWorks argued that the Senate’s legislation was a logical extension of criminal justice efforts in Georgia — which Perdue has backed — but a spokeswoman for the senator rejected the group’s comparison.

“Sen. Perdue supports Gov. [Nathan] Deal’s efforts to focus on rehabilitating first-time, low-level drug offenders in Georgia’s state prison system since that is where first-time, low-level offenders are primarily incarcerated,” spokeswoman Megan Whittemore said. “So comparing the state and federal prison populations is an apples-to-oranges comparison.”

“Instead of focusing on real consensus reforms that promote rehabilitation and reduce recidivism, this bill will instead expose American communities to thousands of drug traffickers and other violent felons,” Cotton said. “It is the victims of crime who will bear the costs of this dangerous experiment in criminal leniency and every community’s law enforcement officers who must deal with that cost daily.”

The next step for the Senate coalition behind the bill will be to persuade Senate Majority Leader Mitch McConnell (R-Ky.) to take up the legislation this year. Speaker Paul Ryan (R-Wis.) has supported criminal justice legislation moving on a parallel track in the House, and the White House backs the effort.

And away from Capitol Hill, two former aides to Senate Majority Whip John Cornyn of Texas — another key Republican supporter — launched a new conservative arm of the U.S. Justice Action Network, a broad coalition of outside groups that has pushed hard for criminal justice reform. The new branch, called Conservatives for Safety & Opportunity, will be led by Cornyn alums Brian Walsh and Rob Jesmer to mobilize conservatives in favor of the bill.

One issue unaddressed in the Senate compromise is the issue of mens rea reform — an overhaul of laws governing criminal intent. The divisive issue has been left out of the Senate legislation since Democrats would not support it. But criminal justice reform efforts in the GOP-led House include mens rea reform.

Grassley said he has not spoken directly with McConnell to push the majority leader to take up the legislation. Supporters acknowledge that floor time is scarce, particularly as Senate Republicans push for a full appropriations process that could last as long as 12 weeks.

A spokesman for McConnell said he had no comment on the revised legislation.

Cornyn, who is McConnell’s top deputy, said the Republican leader is committed to the appropriations process. “But let me just say that if there is floor time that opens up, we want to make sure that we’re one of the candidates for consideration,” Cornyn added.